The O(dd) Story of Massive Supergravity

TL;DR

Kaloper and Myers show that generalized Scherk-Schwarz reductions of heterotic string theory on a $d$-torus preserve a manifest $O(d,d+16)$ duality structure in the reduced action while introducing mass parameters that act as both scalar-potential generators and nonabelian structure constants. By organizing these masses into an antisymmetric tensor $f_{abc}$, they obtain a unified, duality-covariant framework describing massive gauged supergravities across reductions driven by internal fluxes, twisted tori, and all mass sources, with a consistent gauge algebra and Jacobi constraints. Duality transformations must also transform the mass parameters, so U-duality maps between reduced theories rather than spontaneously breaking. The work clarifies how geometry (twists), fluxes, and axions generate masses and shapes the moduli space, potentially reducing to a discrete duality subgroup $O(d,d+16, obreak \\mathbb{Z})$ and offering a unified picture of diverse massive supergravities in string theory.

Abstract

The low energy effective action describing the standard Kaluza-Klein reduction of heterotic string theory on a d-torus possesses a manifest O(d,d+16) symmetry. We consider generalized Scherk-Schwarz reductions of the heterotic string to construct massive gauged supergravities. We show that the resulting action can still be written in a manifestly O(d,d+16) invariant form, however, the U-duality transformations also act on the mass parameters. The latter play the dual role of defining the scalar potential and the nonabelian structure constants. We conjecture that just as for the standard reduction, a subgroup of this symmetry corresponds to an exact duality symmetry of the heterotic string theory.